Question 35.PE.NAQ.5: For one of the values of gain factor (K) for which the contr......

The characteristic equation can be rewritten as

s² + Ks + (2k – 1) = 0

The Hurwitz determinants are

\begin{aligned}\Delta_1 &=K \\\Delta_2 &=\left|\begin{array}{cc}K & 0 \\1 & 2 K-1\end{array}\right| \\\left|\Delta_2\right| &=(2 K-1) K=2 K^2-K\end{aligned}

For |Δ _1| and |Δ _2| to be positive, K > 0 and (2K − 1) > 0. This gives K > 0 and K > 1/2. Thus, the system is stable if K > 1/2.